Let f(x) = x² – 8x. (A) Find the slope of the secant line joining (2, f (2)) and (7, f(7)). Slope of secant line =

Q: Determine the values of x where a curve y = x3 - 3x2 - 9x+ 12 has horizontal angent lines.

A: Given,         y=x3-3x2-9x+12

Q: In the open interval 0, find the point where the slope of the curve y =tanx is 4?

A: in the open interval 0,π2, we have to find the point where the slope of the curve y=tanx is 4. the…

Q: Determine the slope of the curve y =1/x+1 at point (−2,−1).

A:

Q: For Exercise, find the slope of the secant line pictured in red. 6--y = f(x) %23 (3, 4) (1,1)" ! 2 3…

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Q: If ƒ′(x) = 3x + 2, find the slope of the line tangent to the curvey = ƒ(x) at x = 1, 2, and 3.

A: Slope of the tangent line is the derivative of the given function at the given point. Therefore…

Q: Find the equation of the line normal to x3y-2xy2= - 4 at the point (-2,1)

A:

Q: Find the slope of the tangent line to the curve - 2x2 + læy+ 3y = - 83 at the point (- 2, – 3).

A:

Q: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x

A: Rule:-equation of line passing thraught (x1,y1) and (x2,y2) is y-y1=y2-y1x2-x1(x-x1)

Q: 3. Find the tangent lines and normal lines to the curve y = x4 - 4x3 + 6x2 – 4x + 3 with slope…

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Q: What is the slope of the curve y = x2 (x + 1)3 at (1, 8)?

A:

Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

A:

Q: Find equations of the tangent lines (in slope-intercept form) to the curve y = x-1 that are parallel…

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Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of y/x2 at any…

A:

Q: What is the slope of the secant line that passes through the points(a, f(a)) and (b, f(b)) on the…

A: Given: The secant line passes through the points a,fa  and  b,fb. Concept used: The slope of a line…

Q: Find the slope of the tangent line to the curve – 2a2 + xy + 4y³ = - 6 3 at the point (- 2, 1).

A:

Q: Q3: Find equations of all lines having slope (-1) that are tangent to the curve y = 1/(1-x)

A: y=11-x Also, the given Slope is -1

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

A: Curve y=ax3+bx2+cx+d is tangent to the line y=3x+8 at the point (-2,3). The curve y=ax3+bx2+cx+d has…

Q: 2. Estimate the slope of Ix) at the point: a) where x = 3 b) where x = 2 YA fx) 4 3 2 1 2 3 4 5 6 1.

A:

Q: At what point on the curve x = 3t2 + 2, y = t3 – 2 does the tangent line have slope ? (х, у)

A: Slope of the line = dy/dx To get dy/dx, first get dx/dt then get dy/dt. Now divide dy/dt by dx/dt.5

Q: At the two points where the curve x² – xy + y² = 36 crosses the x-axis, the tangents to the curve…

A: Given equation of the curve is: x^2 - xy + y^2 = 36 ..................... (1) Differentiating above…

Q: Find the slope of the curve x²+y²-6x+10y÷5=0 at point (1, 0)

A:

Q: Determine slope of a curve y = x³ + 1 at x = 1

A: Given,           The slope of the curve y=x3+1  at x=1.

Q: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given, the curve y = ƒ(x) in the xy-plane that passes through thepoint (9, 4) and whose slope at…

Q: Find the slope of the line tan gent to the curve of 2y³ + xy + 1 = 0 at the point (-3, 1) .

A:

Q: Find the equation of the family of curve whose slope at any point (x,y) is (x+1)/(y-1)

A:

Q: Find the slope of the curve y=x4 at x=3.

A: Find the slope of the curve y=x4  at    x=3.

Q: Compute the slope of the secant line containing the points (1, f (1)) and D) on the graph of f (x) =…

A:

Q: What is the equation of the line tangent to the curvev= x² – 1 at the point -2,3) y = x+ O y=-4x +…

A:

Q: Show that the slope of the secant line for f(x) = x 3 - 2x over[5,x] is equal to x 2 + 5x + 23. Use…

A: Given: y=fx=x3-2x; 5,x we know that slopem of secant for any given functionfx over a,b is given by…

Q: Find the equation of the tangent and normal line using the stipulated conditions   1.) y = x2 - 5x…

A: Given the equation is y = x2 - 5x The point of intersection line y=6 The equation of the tangent is…

Q: Find the curve in the xy-plane that passes through the point (4,8) and whose slope at each point is…

A: The curve in the xy-plane that passes through the point (4 , 8 ). Slope at each point is 3√x . We…

Q: Find the slope of the curve: y= x^2/x^2 -1 at x=2

A: Slope of curve is the derivative of curve at the point .  Slope = m = ( dy/dx ) | x = a

Q: 4. Find the slope of the given function y3 = 4x with points (1, 2) using long method. Plot the curve

A: The solution are next step

Q: Find an equation of the curve that passes through the point (0, 6) and whOse slope at (X, y) is X/y.

A: Given that: Slope of the curve at (x, y)=xy

Q: The slope of the curve y=x' +3x² – 6x +5 at (1,3) is -

A:

Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

A:

Q: The slope of the curve y^2-xy-3x=1 at the point (0,-1)

A:

Q: Find the slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

Q: Find equations of all lines having slope -1 that are tangent to the curve y = 1/(x - 1).

A: Given, y=1x-1 Slope,m=-1

Q: Find an equation of the curve that passes through the point (0, 4) and whose slope at (x, y) is x/y.

A: Solution:find the equation of curuepasses through the point (0,4)slope of cwue is xydydx=xyy dy=x…

Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

A:

Q: Find the points on the graph of x5/2 + y5/2= 1 where the slope of the tangent line is -1.

A: Topic:- application of derivatives

Q: Find the slope of the line normal to the curve y x3 – 2x + 1 at x = 2

A: Our Aim is to find the slope of the line normal to the curve y=x3-2x+1-(i) at x=2.

Q: What is the slope of the line tangent to the curve y = x4 – 8x3 + 22x2 – 24x + 9 at x = 1?

A:

Q: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

A:

Q: ]Find the x-intercept of the curve that passes through the point (0,2) and whose slope at (x,y) is…

A:

Q: 4) Find the slope of the curve y = 3x + 1 at point P (1,2)

A: We need to find slope of curve at given point.

Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.