Both a function and its derivative are given. Use them to find the relative maxima.
E) no relative maxima

Question

Both a function and its derivative are given. Use them to find the relative maxima.  
E) no relative maxima

Quizplus · Accepted Answer

To find the relative maxima, we need to look for critical points where the derivative changes sign from positive to negative. Setting the derivative equal to zero, we get:

11ea984b_b210_1979_9029_51b83be22b92_TB4005_11 = 3x^2 - 12x + 11 = 0

Solving for x using the quadratic formula, we get:

x = (12 ± √8)/6

x ≈ 1.27 or x ≈ 0.73

These are the critical points. Calculating the values of the original function at these points, we get:

11ea984b_b210_1978_9029_995f8cf4ec6a_TB4005_11 ≈ 5.23 and 11ea984b_b210_1978_9029_996d0c58aae6_TB4005_11 ≈ 4.43

Since the derivative changes sign from positive to negative at x ≈ 1.27, this is a relative maximum. Therefore, the correct answer is B.

Both a Function and Its Derivative Are Given