Slope of a Tangent Line
Find the derivative of the function
f(x) = 3x2 - 6x + 788
f'(x) = 6x-6
Find the absolute maximum of f(x) from the interval [0, 2].
f(x) = x2
Absolute Max: 4 at x = 2
Evaluate the Integral
∫03 (4x)dx
18
Find the average value of f(x) = 6x on the interval [0, 4].
12
Find the slope of the line tangent to the function g(x) = 2x3 - 4x2 + 6x at x = 3
g'(3) = 36
Find the following limit.
limx→∞ (x2)/(3x)
The limit = ∞
Find all absolute maximums for the function g(x) = 3sin(x) + 2 from the interval [0, 2π]
5 at x = π/2
Find the integral for the equation of g(x) using the bounds [0, 2]
g(x) = (3x2 - 2x + 1)
6
Evaluate the average value of g(x) on the interval [0, 3].
g(x) = 3x2 - 2x
6
Find h'(5)
h(x) = x3ex + 2x
h'(5) = 200e5 + 2
or
h'(5) = 29684.632
The limit = 6
Find the absolute minimum of h(x) from the interval [-1, 3].
h(x) = x2 - 4x + 5
1 at x = 2
Find the integral of h(x) using the bounds [π, 2π]
h(x) = 3cos(x)
0
Evaluate the average value of h(x) on the interval [2, 4].
h(x) = x3 - 6x + 1
13
Find j''(2)
j(x) = x4 - 4x2 + ln(x)
j''(2) = 39.75
or
j''(2) = 159/4
Find the limit PLEASE.
limx→∞ (5x2 - 3x + 26)/(2x2 - 9)
The limit = 5/2
Find the minimum value(s) for the function j(x) on the interval [0, 4].
j(x) = (x2 + 9)/x
6 at x=3
Evaluate the following integral.
∫0π/2 [sin(2x)]dx
1
Find the average value of j(x) = 5x2 + 7x - 3 on the interval [-2, 2].
11/3
Find the equation of the line tangent to the function k(x) = cos(x2+5) + sin(x) at x = 0
y = x + cos(5)
or
y = x + 0.284
Evaluate the limit.
limx→-4 (x2 + 2x - 8)/(x+4)
The limit = -6
Find the absolute maximum value(s) for the function on the interval [-1, 2].
k(x) = 2x3 - 3x2 - 12x + 1
8 at x = -1
Solve the following definite integral equation.
∫24 (2x3+3x2+4x+5)dx
210
Find the average value of k(x) on the interval [0, 5]
k(x) = x2 + ex
(122/15) + (e5/5)
or
37.816