# Suppose that f(t) = t^2 + 2t - 4. A) What is the average rate of change of f(t) over the interval...

## Question:

Suppose that {eq}f(t) = t^2 + 2t - 4 {/eq}.

A) What is the average rate of change of {eq}f(t) {/eq} over the interval 1 to 2?

B) What is the (instantaneous) rate of change of {eq}f(t) {/eq} when {eq}t = 1 {/eq}?

## Average Rate of change and Instantaneous Rate of Change:

Average rate of change, (A(x)), is finding how much the function changes over time. It is the same like finding the slope of line joining two points.

Therefore, average rate of change of {eq}f(t) {/eq}over {eq}[a,b] {/eq} is, {eq}A(t) = \frac{f(b)-f(a)}{b-a} {/eq}

Instantaneous rate of change of a function {eq}f(t) {/eq} is the rate of change of {eq}f {/eq} at the instant {eq}t {/eq}. It is same as the tangent to {eq}f {/eq} at the point {eq}t {/eq}. In other words, {eq}f' {/eq} at the point {eq}t {/eq}.

## Answer and Explanation:

{eq}f(t) = t^2 + 2t - 4 {/eq}

Average rate of change of {eq}f(t) {/eq} over {eq}[a,b] = [1,2] {/eq} is given by,

{eq}A(t) =...

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