Assume f and g are differentiable functions with h(x) = f(g(x)). Suppose the equation of the line tangent to the graph of g at the point (2,3) is y= -4x+11 and the equatic to the graph of f at (3,1) is y= 3x-8. a. Calculate h(2) and h'(2). b. Determine an equation of the line tangent to the graph of h at the point on the graph where x= 2. a. h(2) =

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A: The given curve is: f(x)=6x+15-15ex

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A: Given,        The line y=3x+k is tangent to the curve y=x3

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A: We know that :ddxf(g(x))=f'(g(x))g'(x)

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Q: For which value(s) of x does f(x)=−x^3/3−2x^2+3x−8 have a tangent line of slope 7?

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A: The derivative of a function at a point represents the slopeof tangent at that point .

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A: Explanation of the answer is as follows

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A: Given curve is Differentiating with respect to x , we get Now, we will find f(4) and f'(4)

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A: By using the derivative and slope intercept form required tangent equation is :

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A: Given function, fx=x3-5x+1 Tangent is passing through (x1,y1) (1,-3).

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A: Find the equation of the tangent line of fx=8x+3 at the pint (4,19).

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A: Equation of the line in slope-point form is:        m = slope (x1, y1) = point on the line

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A: Given function,f(x)=3x+10,Aim:- To find the slope of the tangent of the curve f(x) at (-3,1)Let…

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A: This question can be solved using the concept of tangent and normal.

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A: Given  y=ax2-6x+1find derivativey'=ddx(ax2-6x+1)y'=2ax-6+0y'=2ax-6at x = 1y'=2a(1)-6y'=2a-6

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A: The given function is y=e3x

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A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

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A: Consider the provided function, y=5x+2 Find the value of f3  and  f'3 at a=3. y=5x+2 We can write…

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A: WE area asked to find h'(1)

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A: Please refer the attached image for complete solution.

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A: equation of tangent line