Question

If f(x) = 3x2 − x + 5, find the following

f(2) =

f(−2) =

f(a) =

f(−a) =

f(a + 1) =

2f(a) =

f(2a) =

f(a2) =

[f(a)]2 =

f(a + h) =

Answer #1

The answer for above problem is explained below.

a)
Find f(x) is f(x) is differentiable everywhere and
f'(x)= { 2x+8, x<2
3x2, x>2
given f(1)=1
b)
the point (-1,2) is on the graph of
y2-x2+2x=5. Approximate the value of y when
x=1.1. Then use dy/dx and
d2y/dx2 to determine if the point (1,-2) is a
max, min, or neither.

Find f(x).
f ''(x) = 1/3x3 −
3x2 + 6x

Suppose that f(2) = −4, g(2) = 2, f '(2) = −5, and g'(2) =
1.
Find h'(2).
a. h(x)=2f(x)-5g(x)
h'(2)=?
b. h(x)=f(x)g(x)
h'(2)=?
c. h(x)=f(x)/g(x)
h'(2)=?
d. h(x)=g(x)/1+f(x)
h'(2)=?

1. What is a relative min extrema (x,y) for f(x) in f(x) =
2x3+3x2-12x+5 ?
2. Use a number line and test points to show where f(x) in f(x)
= -2x3-1/2 x2+x-3 is concave up and down
3. use a number line and test points to show where f(x) in
2x3+3x2-36x+20 is increasing and
decreasing

Find
(f −1)'(a).
f(x) = 4x3 + 3x2 + 7x +
7, a = 7

Question 1.
Find the equation of the tangent line
of f(x) =3x2-x+2 at x=2
Question 2.
Let g(x)= ln(x) + 3
Is g(x)
increasing at x=1? Justify your answer.
Does
g(x) have any inflection points? Justify your answer

Suppose the derivative of f exists, and assume that f(1) = 4,
and f'(1) = 5. Let g(x) = x^2f(x), and h(x) = f(x)/x-2
a) g' (1) = ??
find the equation of the tangent line to g(x) at x = 1
y = ??
b) h'(1) = ??
Find the equation of the tangent line to h(x) at x = 1
y = ??

f(x) = 3 / [x^2 +1] ; g(x) = x + 1.
2a: f o g(x) = ?
2b: g o f(x) = ?
2c: Domain of f ?
2d: Domain of g ?
2e: Domain of f o g ?
2f: Domain of g o f ?

Find the values of a function f(x) if
f(x) = 2x + 5, for
f(2), f(4),
f(k), and f(x2 +
2)
The difference quotient of a function is given by:
limh0f(x)
fx+h-f(x)h . Find the
difference quotient of, f(x) = 2x + 3 and f(x) = x2 +
2
a. Prove that h(x) and k(x) are inverses of each other when
h(x) =x+213 and k(x) = 3x + 21

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

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