Question

Consider the following.

f(x) = 4x^{2} + 8x − 18

(a) Find the derivative, by using the definition.

f '(x) =

(b) Find the instantaneous rate of change of the function at any
value.

f '(x) =

Find the instantaneous rate of change of the function at the
value

x = −3.

f '(−3) =

(c) Find the slope of the tangent at the value

x = −3.

Answer #1

Consider f(x) = x2 – 8x. Find its derivative using
the limit definition of the derivative. Simplify all
steps.
a. Find f(x + h).
____________
b. Find f(x + h) – f(x).
____________
c. Find [f(x + h) – f(x)] ÷ h.
____________
d. Find lim (hà0) [f(x + h) – f(x)] ÷ h.
____________
e. Find an equation of the line tangent to
the graph of y = x2 – 8x where x = -3. Present your
answer...

Please Find: f(x)=x2+2
1) The derivative of f(x) using the limit definition:
2) The instantaneous rate of change at x=3:
3) The equation of the tangent line at x=3:
Please write out all the steps clearly.

Please Find: f(x)=x2+2
1) The derivative of f(x) using the limit definition:
2) The instantaneous rate of change at x=3:
3) The equation of the tangent line at x=3:
Please write out all the steps clearly.

Part 1) Find the derivative of the function
f(x)=e^((x^2)/(x^2+4))
Part 2) Find the derivative of the function
f(t)=(e(^t^2)+4t)^4
Part 3) Find the derivative of the function y=log6sqrt(8x+3)
Part 4)
The number x of stereo speakers a retail chain is willing to
sell per week at a price of pp dollars is given by
x=78sqrt(p+24) -390
Find the supply and instantaneous rate of change of supply when
the price is 75 dollars.
Supply = 386
Instantaneous rate of change of supply...

Consider the function f(x) = (8x^3-4x)^3
(a) Find the derivative
(b) Find critical numbers of f. (Hint there are 5 critical
numbers) Round your answers to three decimals.
(c) Fill out the sign chart for the derivative below. Please
label the axis as appropriate for your critical numbers.
(d) What are the relative max(es) and min() of f?

Let f(x)=3x2+10x+3.
a) Find the derivative of f(x) using the definition of the
derivative.
b) Find the equation of the tangent line at point x=−1

Show that the derivative of f(x) = 6+4x^2 is f' (x)=8x by using
the definition of the derivative as the limit of a difference
quotient.

find the derivative using a definition of the derivative (h) of the
following function
f(x)= x/(x-1)

Find the derivative of the function using the definition of
derivative.
f(x) =
1
5
x −
1
6
f '(x) =
B,
f(x) =
2.5x2 − x + 4.8
f '(x)
=
C,
f(x) =
3x4
f '(x)
=
D,
If
f(t) =
3
t
and
a ≠ 0
, find f '(a).
f '(a) =

a) find the derivative of xcos(x^2) using
any method.
b) find the derivative of f(x) = sqrt(3-x) using only the
definition.

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