f(x)=2x^4-5x^3-9x^2+32x-20
-Find the
A: Intercepts
B: equation of asymptote
C: local extrema
D: Inflection Point
E: All end behaviours and behaviours around the
asymptote
Given f(x,y) =(x3y- 2x2y)
a) find the directional derivative of f(x,y) at (1, 2) in the
direction of <-3,4>
b)find the maximum value of directional derivative at (2,4) and
the direction in which this occurs
consider the function
f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and
f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) find the local maximum and minimum values. Justify your
answer using the first or second derivative test . round your
answers to the nearest tenth as needed.
b)find the intervals of concavity and any inflection points of
f. Round to the nearest tenth as needed.
c)graph f(x) and label each important part (domain, x- and y-
intercepts, VA/HA, CN, Increasing/decreasing, local min/max values,
intervals of concavity/ inflection points of f?
Use the given function, its first derivative, and its second
derivative to answer the following:
f(x)=(1/3)x^3 - (1/2)x^2 - 6x + 5
f'(x)= x^2 - x - 6 = (x+2)(x-3)
f''(x)= 2x - 1
a) What are the intervals of increase and the intervals of
decrease
b) Identify local min and max points
c) What are the intervals where the function is concave up,
concave down and identify the inflection points
. Let f(x) = 3x^2 + 5x. Using the limit definition of derivative
prove that f '(x) = 6x + 5
Then, Find the tangent line of f(x) at x = 3
Finally, Find the average rate of change between x = −1 and x =
2