Math Problem Statement

Let \( g(x) = \int_0^x f(t) \, dt \), where \( f \) is the function whose graph is shown. (a) Evaluate \( g(x) \) for \( x = 0, 5, 10, 15, 20, 25, \) and \( 30 \). (b) Estimate \( g(35) \). (c) Where does \( g \) have a maximum and a minimum value?

Solution

To solve this problem, let's go through each part step-by-step. We have g(x)=∫0xf(t) dtg(x) = \int_0^x f(t) \, dt, where ff is represented in the graph, and we are required to evaluate g(x)g(x) for specific values of xx, estimate g(35)g(35), and identify the minimum and maximum values of g(x)g(x).

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Math Problem Analysis

Mathematical Concepts

Calculus
Integral Calculus
Area under the curve

Formulas

\( g(x) = \int_0^x f(t) \, dt \)

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12

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