Math Problem Statement

Given that f(6) = 7, write an expression for f(x) that involves an integral. Use this expression to find the absolute minimum value and the absolute maximum value of f on the closed interval 0 ≤ x ≤ 9. Justify your answers. Use a theorem to investigate two graphs. Find the value of ∫2^3 x f'(g(x)) dx of inner function, cancel the y - change backs.

Solution

It looks like the image contains a set of calculus problems. Let me break down the contents:

  • (c) asks you to write an expression involving an integral for a function f(x)f(x), then use this expression to find the absolute minimum and maximum values of f(x)f(x) over the interval 0≤x≤90 \leq x \leq 9, justifying your answers.
  • (d) asks you to find the value of the integral ∫23xf′(g(x)) dx\int_2^3 x f'(g(x)) \, dx, with some instructions about identifying the inner function and changing variables.

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Math Problem Analysis

Mathematical Concepts

Calculus
Integral Calculus
Differentiation
Theorems in Calculus

Formulas

f'(x)
∫a^b f(x) dx

Theorems

Mean Value Theorem
Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12

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