A body is moving in a straight line with a speed v(t) = 2t-4 m/S Find the distance traveled with an interval of [1,6] Then find the distance of the body after (4) seconds from the start of the movement

Q: Find the equation of the tangent and normal line of the function y^3 +3xy + x^4 = 5 at the point (1,…

A: y3+3xy+x4=5 Differentiating with respect to x, we get…

Q: The tangent line to the graph of y = h(x) at the point ( -1, 4) passes through the point (3, 6).Find…

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Q: Find the points on the curve  y = x3 + 3x2 − 9x + 2 where the tangent is horizontal.   smaller…

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Q: The point (1,2) is on the curve y=f (x), and at any point (x,y) on the curve the tangent line has a…

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Q: The curves f(x) = x + 2x + 5 and g(x) - x + 3 intersect at the point ( – 2, 5). Find the acute angle…

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Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 5  where the tangent line is horizontal. (x,…

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Q: =2(3x2)^ has two horizontal tangent lines. Find equations for both of them.

A: y=23x2xy'=2ln3x2+23x2xLet the tangent line equation is given byy-y1=mx-x1y-y2=m1x-x2m=m1=0...as…

Q: The tangent line to the graph of y = h(x) at the point (-1, 7) passes through the point (5, 4). Find…

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Q: Find the length of the curve defined by 2? = 2y3 from x = 0 to x = 4:|| %3|

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Q: Find the exact length of the curve on the given interval. Show at least 3 steps to justify your…

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Q: Find the point on the graph of y = x3 such that the tangent at the point is parallel to the line y –…

A: Consider a graph: y=x3……1   Equation of line parallel to the tangent of above equation is:…

Q: The slope of the tangent line at any point (x, y) on the curve 3x2 -2x+7 and the point (1, 3) is on…

A: Please refer the attached image for complete solution. THANK YOU.

Q: The curve y = a x 2 + b x + c passes through the point ( 1 , 2 ) . The line y = 2 x + 1 is tangent…

A: Given that the curve passes through a point.

Q: The curves f(x) = x² + 2x + 5 and g(x) intersect at the point (– 2, 5). - x + 3 Find the acute angle…

A: Given that ,  fx=x2+2x+5  and ,  gx=-x+3 To find : the acute angle of intersection of curves. The…

Q: the tangent line to the graph (x^2 + 4)y = 8 at the point (2, 1).

A: Use formula of  equation of tangent  line

Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: find an equation of the tangent line f(x)=x+(6/x)    points (x,y)= (-6,-7)

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Q: F(x) = -7+ x2 INTERUAL-ピ-3 -2. AUERAGE RATE of

A: Given query is to find the rate of change for the given interval.

Q: Find the point(s) on the graph of y = (x2 – 48)e × where the tangent line is horizontal. Identify…

A: Tangent is horizontal that means derivative of f(x) is equal zero.

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 5  where the tangent line is horizontal. (x,…

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Q: The tangent line to the curve y = x3 - 6x2 - 34x - 9 has slope 2 at two points on the curve. Find…

A: Given,  The tangent line to the curve y=x3-6x2-34x-9 has Slope=2 at two points on the curve.…

Q: Find the point where the tangent to the curve y = x +6x + 9x + 7 is parallel to the x-axis. 37.…

A: topic - point at which tangent line is parallel to curve. note : As per bartleby guidelines, we are…

Q: 4. Find the equation of the curve for which y""= 2x³. The slope of the inflectional tangent at (-1,…

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Q: The shortest distance from the point (5, 10) to the curve x2 = 12y is: 5.127 6.445 4.331 3.474

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Q: How many tangent lines to the curve y= x /(x+1) passthrough the point ( 1,2) ? At which points do…

A: Given : y=xx+1  pass through the point (1, 2) To find: The number of tangent lines to the curve  y =…

Q: Find an equation of the tangent line to the curve 2(az² + y³)² = 25(x² – y}) - (a lemniscate) at the…

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Q: 3) Calculate the length of the curve interval [-2₁2]. y = x²/2 on the

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Q: How many tangent lines to the curve y = pass through the point (1, 2)? X + 2 2 At which exact points…

A: Given the curve y=(x)/(x+2) passing through the point (1,2). We need to find at what point does the…

Q: Find the slope of the curve y=x^3-3 at the point ​P(-2,-11​) by finding the limiting value of the…

A: Given,y=x3-3Point P -2,-11The slope of the secant line ism=fb-fab-a

Q: The tangent line to the curve y = 1/3x^3−3x^2+9x+12 is parallel to the line 8x−2y=3 at two…

A: given: the tangent line to the curve y=13x3-3x2+9x+12 is parallel to the line 8x-2y=3 at two points…

Q: 8 17

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Q: Find the length of the curve 9y2=8x3 from x=o to x=12 when y>0

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Q: nd the point (both x and y coordinates) where the tangen

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Q: Find an equation of the normal line to y = x2 at the point (2, 4). (The normal line at a point is…

A: y=x2 Differentiating with respect to x, we get dydx=2x Now slope of the tangent line at 2, 4 is,…

Q: The slope of the tangent line at any point (x, y) on the curve 3x2 - 2x+7 and the point (1, 3) is on…

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Q: The curves f(x) = x² + x + 4 and g(x) = - 5x + 20 intersect at the point (2, 10) Find the acute…

A: Given, fx = x2+x+4  and  gx = -5x+20  intersected at the point  2, 10 We have to find the acute…

Q: A. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of…

A: A. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of…

Q: Find the tangent and normal line to the curve at the specified condition.  3x3 - x2 - 12x + 6 at…

A: Suppose we wish to find the equation of the tangent tof(x) = 3x3 − x2 - 12x +6 the points where the…

Q: 2-In method, we approximate the curve of solution by the tangent in each interval. * Your answer

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Q: A tangent line to y=1/x^2 intersects the x-axis at the point A and the y-axis at point B. What is…

A: Please note: The line tangent to the given function intersects the x-axis at a point A and the…

Q: How many tangent lines to the curve y = pass through the point (1, 2)? X + 6 2 At which points do…

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Q: Find all values of x such that the tangent line to the graph of y 5x2 - 9x + 8 is steeper than the…

A: To determine all the values of x where the slope of the first curve is greater than the slope of the…

Q: How many lines are tangent to both of the circles  x2 + y2 = 4  and  x2 + (y − 3)2 = 1?   At what…

A: Given: The equations of circle are given as, Consider the parametric co-ordinates for the Eq. (A)…

Q: Find the equation of a Tangent line to y = 2x2 – 5x – 1 that is parallel to line x + y –

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Q: The straight line y=x +B is tangent to the graph of f(x) = 2^{x at the point where x = A. Find A and…

A: The staright line y=13x+B is tangent to the graph of f(x)=2x at the point where x = A, we have to…

Q: At which point on the curve y = 1 + 2e^x -3x is the tangent line parallel to the line 3x - y = 5…

A: The given curve is y = 1+2e^x-3x.In order to compute the slope of the tangent line of the curve,…

Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

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Q: 3. The normal line to the curve y = f (x) = 2x² at a point in the first quadrant passes through the…

A: Question is solved.

Q: fa) =x3-6x*+15x-2, Please find for the tangent line to f "x) (8,1)

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.