1:
Given that f(4) = 6 and f'(x) = 2/x2+9 for all x.
a) Use a linear approximation or differentials to estimate
f(4.04)
b) Is your estimate in part (a) too large or too small?
Explain.
2:
a) Given f(x) = (x + 3)sinx, find f'(π) using
logarithmic differentiation.
b) Find the value of h'(0) if h(x)+xsin(h(x))=
x2+4x-π/2
part 1)
Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of f
and determine its inflection point(s).
part 2)
Find the absolute extrema of f(x) = x^4 + 4x^3 − 8x^2 + 3 on
[−1, 2].
f(x) = (2x − 3)(x 2 − 6)
(a) Write formulas for f '(x) and f ''(x).
(b) Find all x-intercepts of f(x). (Exact answers, no
decimals.)
(c) Find all critical points of f(x). (x-values only; y-values
not needed.) Classify them using the 1st or 2nd derivative
test.
(d) Find all inflection points of f(x). (x-values only; y-values
not needed.)
If f(x)=2x^2−5x+3, find
f'(−4).
Use this to find the equation of the tangent line to the parabola
y=2x^2−5x+3 at the point (−4,55). The equation of this tangent line
can be written in the form y=mx+b
where m is: ????
and where b is: ????