Question

Find f(x).

1. f''(x) = (1/3) x^3 −3x^2 + 6x

2. f''(x) = −1 + 6x−12x^2, f(0) = 4, f'(0) = 12

3. f'''(x) = sinx, f(0) = 1, f'(0) = 2, f''(0) = 3

Answer #1

Find only the rational zeros of the following function:
f(x)=x^4+6x^3-9x^2-12x+14

Q) Find f.
f''(x)= −2+36x−12x^2, f(0)=7,
f'(0)=12
f(x)=
Q) Find f
f''(t)=sint+cost, f(0)=2, f'(0)=3
f(t)=
Q) Find f
f''(x)=20x^3+12x^2+4, f(0)=4, f(1)=2
f(x)=

Let f (x) = 3x^4 −4x^3 −12x^2 + 1, deﬁned on R.
(a) Find the intervals where f is increasing, and decreasing.
(b) Find the intervals where f is concave up, and concave
down.
(c) Find the local maxima, the local minima, and the points of
inflection.
(d) Find the Maximum and Minimum Absolute of f over [−2.3]

find the equation of a tangent line(s) to the curve with slope 5
f(x)=x^3 + 3x^2 - 4x - 12
f'(x)= 3x^2 +6x - 4

Find fhe equation of the tangent lines with slope of 5
a) f(x)= x^3 + 3x^2 - 4x -12
b) g(x)= 3x^2 + 6x - 4

1. Given f(x)=2x^3-3x^2+4x+2, find (f^(-1))'(14).
Differentiate and Simplify
2. f(x)=ln(3x) e^(-x^2 ) (Answer with positive exponents
Integrate and Simplify 3. ∫▒(6x^2-5x)/√x dx

the function f given by f(x)=2x^3-3x^2-12x has a relative
minimum at x=

4. Given the function y = f(x) = 2x^3 + 3x^2 – 12x +
2
a. Find the intervals where f is increasing/f is
decreasing
b. Find the intervals where f is concave up/f is concave
down
c. Find all relative max and relative min (state which
is which and why)
d. Find all inflection points (also state
why)

use
the second derivative test to find the reltive extrema if any f(x)=
2x^3-3x^2-12x+5

1. Find and interpret f'(−2)
f(x)=−2x^2−3x+4
f'(-2)=
2. Find and interpret f'(1)and f′'(1)
f(x)= 2/x
f'(1)=
f''(1)=
3. Find and interpret f'(1)and f′'(1)
f(x)=−2√x
f'(1)=
f''(1)=
4. If f(x)=(2x−5)(3x+1) then
f'(1)=
the values of x for which f(x)=0 are _ , _
the values of x for which f'(x)=0 are

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