1. Consider the function f (x) = 2(3x³ – 2x²)5. a. Differentiate the function. b. Find the slope of the tangent line to the graph of the function at the point (1,2). 2. A firm in a competitive market must sell its product for $46 per unit. The total cost function for this product is given by C(x) = 100 + 30x +x?. 10 a. Form the Profit function. b. Find the marginal profit when x = 100 and explain what it predicts.

Q: 18. Find the denvative or the runction y = 2x - 13x + 5 and use it to find an equation of the line…

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Q: The slope of the tangent line to the graph of the function y = 2/x – 6 at (36, 6) is 6 -0.50 0.17…

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Q: 3. Determine the value of b if the slope of the tangent to f(x) = (3x² + 1)(2x² + b) at x =– 1 is –…

A: given,       fx=y=3x2+12x2+b    slope of the tangent, at x=-1      dydx=-16

Q: 15. The constant of proportionality involved in the direct variation of b with c, is 1.2. What is…

A: In this question, c is independent variable where as b is dependent variable. Given, b is directly…

Q: Find an equation of the line L tangent to the graph of f(x) = 8x +1 at x = 1/2.

A: Calculate the y-coordinate of the point where the tangent has to be drawn. Substitute 12 for x in…

Q: 21. Find an equation of the tangent line to the graph of f(x) = x² - 2x at (a) (–2, 8); (b) (1, –1);…

A: fx=x2-2x

Q: 1. Determine the points where the slope of the tangent to the curve: a. f(x) = 1- 3x² is equal to 5…

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Q: If the slope of the tangent line to the graph of y=f(x) at x=a is m(a)=2a+1, and fl-1)=2, then what…

A:

Q: 4. Write an equation of the tangent line to the graph of f (x)=3x+8x at the point where x= 9.

A: Given query is to find equation of tangent to the f(x).

Q: Suppose that the intensity of a point light source is directly proportional to the strength of the…

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Q: 2. Find the equation of the tangent line to the graph of the function at the indicated point. (a)…

A: Explanation of the answer is as follows

Q: 5. Find the equation of the tangent line to the graph of the function f(r) = 5- z at the point where…

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Q: What is the slope of the tangent line that touches the graph of In(y) +e-=3y– 4x at the point A В) з…

A: slope , m=dydx.

Q: Find an equation of the tangent line to the graph of  y = g(x) at x = 2 if g(2) = −3 and g'(2) = 4.…

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Q: Suppose f(3) = 6 and f '(3) = 7. Find an equation of the tangent line to H(x) at x=3. %3D H(x) =…

A: We have,  Hx=x4-7fx, f3=6 and f'3=7 Using the chain rule of differentiation, H'x=x4-7·f'x+fx·4x3…

Q: Find the equation of tangent for the implicit function x3 - xy2 + 3y2 + 4 = 0. at the point (1, 2)

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Q: 2) Find the equation of the tangent line to the graph of x? + (y – x)3 = 9 at the point x = 1.

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Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…

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Q: Find the equation of the tangent line to the graph of the function f (x) = v 4,4 + 12 at the point…

A: Consider the equation

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x^2 −0.01y^2…

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Q: What represents the slope of the tangent to f(x)= √x+3 at x=1

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Q: 34. Find an equation of the line tangent to the graph of f(x) = (2x – 1)(x + 4) at (1, 5).

A: The objective of the question is find the equation of tangent at the point (1,5).

Q: Find the equation of the tangent line to the graph of the function f(x)=(x2+7)(x−2)fx=x2+7x−2 at the…

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Q: Find the slope of the tangent to the graph of fAx) = x + 3x + x at its point of inflection. O a) -3…

A: SOLUTION-

Q: 22. Find an equation of the tangent line to the graph of f(x) = 4 - x² at (a) (-1,3); (b) (0, 4);…

A: Given: f(x)=4-x2 To Find: the equation of the tangent line to the graph at a) (-1, 3) b) (0, 4)…

Q: Suppose that the total cost function, in dollars, for the production of x units of a product is…

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Q: 1) Find the equation of the line tangent to the graph of f(x) = (x² + 1)(x³ + 1) at the point where…

A:

Q: Find an equation for the tangent to the curve at the given point. f (x) = 6/¤ – x +1, (36, 1) -

A:

Q: 5. Find the equation of the line tangent to the graph of f(x)= 2x' +4x² – 5x– 3 at | x = -1.

A: f(x)=2x3+4x2-5x-3diff w.r.t xf'(x) =6x2+8x-5now substitue x=-1f'(-1)=6(-1)2+8(-1)-5f'(-1)=-7slope of…

Q: 6. The tangent to the function f(x) = ke2x at x = has slope 2e. Find the value of k.

A:

Q: 19. If an equation of the tangent line to the curve y = ƒ(() at the point where a = 2 is y = 4x - 5,…

A: The given equation of  tangent line at curve y=f(x) at a point is y=4x-5. Now, at point a=2 tangent…

Q: If the slope of the tangent line to the graph of y-f(x) at x=a is m(a)=2a+1, and f(1)=5, then what…

A: m(a)= 2 a + 1 f'(x) = m(x) = 2x +1  Integrating f'(x) gives f(x); f(x) = 2(x2/2) + x + c f(x) = x2 +…

Q: If y = f(x) has slope  −4  at x = 3, and y value 5 at x = 3, a) write the formula for the tangent…

A: (a) To write: The formula for the tangent line to f(x) at x=3. Given information:  If y = f(x) has…

Q: What is the equation of the tangent line to graph of the function y = e^(3x) at the point (0,1)? O y…

A: The given function is y=e3x

Q: What is the equation of the tangent line to the graph of f'(x) at x = 4, if f(x) = vx? O y = - + O y…

A: Topic:- application of derivatives and tangent equation

Q: 1. Find in Barrow's way the slope of the tangent line to the curve 2x?y + 5x - xy? = 0 at the point…

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Q: Suppose f (x) = (x 2 − 2x) (3x + 2).What is the equation of the line normal to f(i.e., the line…

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Q: The slope of the tangent line to the graph of the function y= 8/T-6 at (36, 42) is O -1.50 6 O 0.67…

A: Slove of the tangent to the function y at point (a,b) is m= y'(a).

Q: a) Find the points at which the tangent line to the graph of function f(x)=2x²-24x+6 has slope equal…

A: Let y=f(x) be any function, then    Slpoe at any point, m = df(x)dx

Q: What is the slope of the tangent line that touches the graph of Iny+e2x-1 = 3y – 4x at the point A 1

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Q: 3 Find the slope of the tangent to the graph of f(x) = /x+5 at the point where x= 4.

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Q: Find the equation of the tangent line to f(x)=4x+x^−1/2+1 at the point (4,35/2)

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = lnx4…

A:

Q: Find the equation of the tangent line to the graph of the function f(x)=(x2+8)(x−3) at the point…

A: Given: y=fx=x2+8x-3 at 0,-24 we know that for finding equation of tangent we need to find slopem of…

Q: Find the values of x for which the gradient of the tangent to the graph of y=f(x) is equal to the…

A: We have to find the values of x for which the gradient of the tangent to the graph of y=f(x) is…

Q: Suppose the curve y=f(x) has a tangent line y=4x-5 at x=1. Consider the function g(x)=2f(x)+x+1.…

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Q: 3. Determine the value of b if the slope of the tangent to f (x) = (3x² + 1)(2x² + b) at x = – 1 is…

A: The formula to find the slope of the tangent to the function f(x) is f'(x).

Q: The slope of the tangent line to the graph of the function y = 8/T- 4 at (16, 28) is O 4 O -1.75 O…

A: Slope : It is the Differentiation of y with respect to x at a given point.

Q: The slope of the tangent line to the graph of the function y = 4/T-6 at (36, 18) is | 0 36.00 O0.33…

A: slope is the first derivative of the function with respect to x.

Q: Find the slope of the tangent line to the graph of the function at the given point. y = In x3 y 5E 4…

A: