Question

The absolute extreme values of the function f(x) = x^3 − 15x^2 + 48x + 9 on the interval [−1, 2] are as follows: Maximum value: f(2) = 2^3 − 15(2)^2 + 48(2) + 9 = 8 − 60 + 96 + 9 = 53 Minimum value: f(−1) = (−1)^3 − 15(−1)^2 + 48(−1) + 9 = −1 − 15 − 48 + 9 = −55 Therefore, the absolute maximum value of the function on the interval [−1, 2] is 53, and the absolute minimum value is -55.

Name: the absolute extreme values of the function fx x3 15x2 48x 9 on the interval 1 2 are as follows maximum value f2 23 1522 482 9 8 60 96 9 53 minimum value f1 13 1512 481 9 1 15 48 9 55 theref 23063
Uploaded: 2022-03-30T02:04:44-08:00
Duration: 2 min 48 s
Channel: Suman Saurav Thakur
Description: the absolute extreme values of the function fx x3 15x2 48x 9 on the interval 1 2 are as follows maximum value f2 23 1522 482 9 8 60 96 9 53 minimum value f1 13 1512 481 9 1 15 48 9 55 theref 23063

          The absolute extreme values of the function f(x) = x^3 − 15x^2 + 48x + 9 on the interval [−1, 2] are as follows:

Maximum value: f(2) = 2^3 − 15(2)^2 + 48(2) + 9 = 8 − 60 + 96 + 9 = 53

Minimum value: f(−1) = (−1)^3 − 15(−1)^2 + 48(−1) + 9 = −1 − 15 − 48 + 9 = −55

Therefore, the absolute maximum value of the function on the interval [−1, 2] is 53, and the absolute minimum value is -55.

Added by Tom-S M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Suman Saurav Thakur

03/30/2022

Step 1

The derivative of f(x) is f'(x) = 3x^2 - 30x + 48. Setting f'(x) = 0 gives us 3x^2 - 30x + 48 = 0. Factoring this quadratic equation gives us (3x - 6)(x - 8) = 0. So the critical points are x = 2 and x = 8/3. Show more…

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The absolute extreme values of the function f(x) = x^3 − 15x^2 + 48x + 9 on the interval [−1, 2] are as follows: Maximum value: f(2) = 2^3 − 15(2)^2 + 48(2) + 9 = 8 − 60 + 96 + 9 = 53 Minimum value: f(−1) = (−1)^3 − 15(−1)^2 + 48(−1) + 9 = −1 − 15 − 48 + 9 = −55 Therefore, the absolute maximum value of the function on the interval [−1, 2] is 53, and the absolute minimum value is -55.