Find an equation of the red line if a=−3, b=9 and an equation of the blue curve is y=x^2+8

Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y =…

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Q: Find the equation of the line tangent to the graph of y = 2x - 8x2 + 2x -6 at x = 2. | %3D

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Q: Show that the x-coordinate of the vertex of the parabola whose equation is y = ax2 + bx + c occurs…

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 64x2 +…

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Q: What is the slope of the tangent line to the graph of the solution of y' = 6√y + 7x³ that passes…

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Q: What is equation of the line tangent to the graph of y = x^3 + 3x^2 + 2 at its point of inflection?

A: Given that, The equation of line is given following, y = x3 + 3x2 + 2 We have to find the equation…

Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: Find an equation of the line tangent to thegraph of ƒ(x) = x3 + 4x at (1, 5).

A: Given: The graph is expressed as fx=x3+4x To Find : Equation of line tangent to 1,5  The equation of…

Q: 3. Suppose that the water level of a river is 50 feet and that it is receding at a rate of 0.75 foot…

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Q: Next There is a line through the origin that divides the region bounded by the parabola y = 4x –…

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Q: Find an equation of the line tangent to the graph of ƒ(x) = (2x - 1) (x + 4) at (1, 5).

A: To findEquation of the line tangent to the graph y=(2x-1)(x+4)  at (1,5)⇒y=2x2+7x-4.

Q: Find the equation of the curve that passes through (- 1, - 6) if its slope is given by %3D dx 15x2 -…

A: dydx=15x2-12xFormula∫xndx=xn+1n+1+C

Q: Help to find the equation of the line tangent to the curve y = 6 / x when x = 3.

A: Given curve is y=6x When x=3 then y=63=2 So, point is (3,2) Equation of tangent line at any point…

Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y = dy…

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Q: There are two lines passing through the point (5,-1) that are tangent to the parabola y = -x^2+4x.…

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Q: A cigar manufacturer produces x cases of cigars per day at a daily cost of 50x(x + 200)>(x + 100)…

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Q: A population of 200 rodents is growing at a rate of 5% per month. What equation model can represent…

A: The exponential growth or decay is modelled using the equation, f(t)=a(1±r)t, where a is the initial…

Q: 1. What is the instantaneous slope of y = 5 at x = 5?

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Q: Find the equation of the curve that passes through the point (8,2) if its slope is given by…

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Q: Find the equation of the curve that passes through the point (8, 6) if its slope is given by dy =6z-…

A: We have to find y

Q: Find the slope of the curve at the given point: 1. ( X+2y)^2 =x+10 at (-1, 2)

A: Here I am attaching image so that you understand each and every step. slope of the curve given at…

Q: Find the equation of the curve that passes through the point (7,3) if its slope is given by dy = 7x…

A: As per our company's policy, we can solve first question only. Please repost other question…

Q: one leg of a right triangle is 1 in/min and the other leg increases 2 inches per min. What is the…

A: Let the first leg of the right triangle be a and the other leg be b. Let the hypotenuse of the right…

Q: Find the slope of the curve at the point (2,3) * x³ 2x + 1 3/2 1 O 1/2 O 1/4

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Q: From the early 1980's through 2012，the number of adults enrolled in Bachelor's Degree programs has…

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Q: Find the slope of the curve at the point where 0 = 4

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Q: Find the equation of the line that is tangent to y = 2log3(x + 1) and is perpendicular to the line y…

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Q: Suppose the percent of males who enrolled in college within 12 months of high school graduation is…

A: Given:         Percent of males enrolled in college is    y= -0.126x + 55.72         Percent of…

Q: Find the equation of the curve that passes through the point (5,4) if its slope is given by…

A: dydx=5x-2dy=5x-2dxIntegrate on both sides

Q: Find an equation of the line that is tangent to the grapt Function Line 4x-y+2 = 0

A: Since, we have been given up the function:-f(x)=2x2 -(i)Differentiating equation-(i), with respect…

Q: Find the equation of the line tangent to the graph f(x)= (lnx)5 at x=5

A: First find slope then use equation of tangent tangent line

Q: Find the equation of the curve that passes through the point (8, 4) if its slope is given by dy = 5x…

A: At (8,4) the value of C will be: 4=5(8)22-4(8)+C4=160-32+CC=-124 So the equation will be…

Q: Find the equation of the curve that passes through the point (8, 4) if its slope is given by dy = 5x…

A: Using variable separable form of Differential equation.

Q: Suppose the sales of a company are given by S=200x+800 where x is measured in years and x=0…

A: To find the sale of a company S where x=0.

Q: Find the equation of the line tangent to the graph of y = 4x'-9x-7 at the point (1,8).

A: Method to find tangent at a point of any curve.

Q: 2 5. Write the equation of the line tangent to y=4-x when x=-1.

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Q: Find the equation of the line tangent to the graph of y=4ln(x) at x=3.

A: Equation of tangent line

Q: Find the equation of the curve that passes through the point (3, 8) if its slope is given by dy 3x –…

A: We have to find equation of curve

Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

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Q: 4. r(x) = 3x) (1 - x)(-/-)

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Q: find the slope of the line tangent tothe graph of ƒ(x) = -5x + 1 at the point (1, -4).

A: We have to find slope of tangent line to the graph of fx=-5x+1 at the point 1, -4. We know that…

Q: What is the slope of the tangent line to the graph of the solution of y' = 3√√y + 7x³ that passes…

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Q: Find the equation of the curve that passes through the point (6,6) if its slope is given by dy/dx =…

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Q: Find the equation of the family of curve whose slope at any point (x,y) is 3x^2+4

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Q: Calculate the second and the third derivative of y = 5x- 9 y": y"

A: Using derivatives rule & formula.

Q: Determine the equation of the line tangent to the graph of y 5 when x = 9. 2+ Va

A: Given Data The equation is y=52+x. The value of x is x9=9.   Differentiate the equation y=52+x with…