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Find the derivative f 'of f and tangent line

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Let f(x) = x2 + 4x.
(a) Find the derivative f 'of f.
(b) Find the point on the graph of f where the tangent line to the curve is horizontal.
Hint: Find the value of x for which f '(x) = 0.
(c) Sketch the graph of f and the tangent line to the curve at the point found in part (b).

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.
f(x)=7x-3x^2 at (-1,-10)

Use the Intermediate Value Theorem to find the value of c such that f(c) = M. f(x)=x^2-x+1 on [1,8]; M=43.

The final question is in the attachment with a graph attached to it.

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Solution Summary

To find the tangent line equation, it is important to find derivative f' first. To check if function is continuous or discontinuous, it is important to look at the transition point.

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Determine the values of x, if any, at which the function is discontinuous. At each number where f is discontinuous, state the condition(s) for continuity that are violated. (Select all that apply.)

(Select all that apply.)

The function f is discontinuous at x=0 because f is not defined at x=0

The function f is discontinuous at x=0 because f (x) does ...

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