Math Problem Statement

Berapa nilai maksimum dari fungsi f(x) = 3x^5 - 5x^3 + 2 pada interval [-1.2, 1.2]?

Solution

The function provided in the image is f(x)=3x55x3+2f(x) = 3x^5 - 5x^3 + 2, and the interval is [1.2,1.2][-1.2, 1.2]. You're being asked to find the maximum value of the function within this interval.

Looking at the graph:

  1. The graph appears to reach its peak near x=1x = 1, where the value of the function is close to 4.5.
  2. From this observation, it can be inferred that the maximum value of the function on the given interval is approximately 4.

Thus, the correct answer to the question "Berapa nilai maksimum dari fungsi tersebut?" is:

D. 4

Would you like me to provide more details on how to calculate this algebraically, or any other explanation?

Here are 5 related questions to think about:

  1. How can you calculate critical points for this function algebraically?
  2. What is the derivative of the function f(x)=3x55x3+2f(x) = 3x^5 - 5x^3 + 2?
  3. How do you verify whether a critical point is a maximum or a minimum?
  4. How does the interval [1.2,1.2][-1.2, 1.2] affect the extrema of the function?
  5. How can you approximate values using graphing tools?

Tip: When finding maxima or minima of a function, always check the critical points and the endpoints of the interval.

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Math Problem Analysis

Mathematical Concepts

Calculus
Polynomial Functions
Maximum and Minimum Values

Formulas

First derivative of the function: f'(x) = 15x^4 - 15x^2
Critical points: Solve f'(x) = 0 to find where the function's slope is zero
Use the second derivative or graph analysis to determine the nature of critical points (maximum or minimum)

Theorems

First Derivative Test
Second Derivative Test
Extreme Value Theorem

Suitable Grade Level

Grades 11-12 (Pre-Calculus/Calculus)