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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.

https://brainmass.com/math/derivatives/derivative-tangent-line-456914

## SOLUTION This solution is FREE courtesy of BrainMass!

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 not exist.

The function f is discontinuous at x=0 because f (x) exists, but this limit is not equal to f (0).

The function f is continuous everywhere because the three conditions for continuity are satisfied for all values of (x).

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Use the Intermediate Value Theorem to find the value of c such that f(c) = M.

c = 7

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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.

m = 13
y = 13x+3

Let f(x) = x2 + 4x.

f(x) = x2 + 4x (a) Find the derivative f 'of f.
f '(x) = 2x+4

(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.

(x, y) = (-2,-4)

(c) Sketch the graph of f and the tangent line to the curve at the point found in part (b).

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