f(x) = 16x^4 - 8x + 4
-1
a. 24
b. 29
c. 28
d. 4
e. -3
-1
a. 24
b. 29
c. 28
d. 4
e. -3
-
First you need to find the maximum and minimum values.
Candidates for max/min are the two end points of the range, and any point in between where the derivative equals zero.
First, the end points:
f(-1) = 16 + 8 + 4 = 28
f(1) = 16 - 8 + 4 = 12
Next, let's look for where the derivative equals zero:
64x^3 - 8 = 0
x^3 = 8/64 = 1/8
x = 1/2, which lies inside the range.
f(1/2) = 16*(1/16) - 8*(1/2) + 4 = 1 - 4 + 4 = 1
Thus, the maximum value is 28 and the minimum value is 1,
so the sum of the maximum and minimum values is 29.
The correct answer is B.
Hope that helps!
Candidates for max/min are the two end points of the range, and any point in between where the derivative equals zero.
First, the end points:
f(-1) = 16 + 8 + 4 = 28
f(1) = 16 - 8 + 4 = 12
Next, let's look for where the derivative equals zero:
64x^3 - 8 = 0
x^3 = 8/64 = 1/8
x = 1/2, which lies inside the range.
f(1/2) = 16*(1/16) - 8*(1/2) + 4 = 1 - 4 + 4 = 1
Thus, the maximum value is 28 and the minimum value is 1,
so the sum of the maximum and minimum values is 29.
The correct answer is B.
Hope that helps!