markush35q

Answered question

2022-04-03

Suppose that $f\left(x\right)={t}^{2}+3t-7$. What is the average rate of change of f (x) over the interval 5 to 6?

Answer & Explanation

jmroberts70pbo2

Beginner2022-04-04Added 10 answers

Explanation:
The average rate of change of a function is the same as the total change over the total time, i.e. the rate is
$\stackrel{―}{r}=\frac{\mathrm{△}f\left(x\right)}{\mathrm{△}x}=\frac{f\left(6\right)-f\left(5\right)}{6-5}=f\left(6\right)-f\left(5\right)=47-33=14$

Melody Gamble

Beginner2022-04-05Added 10 answers

Explanation:
the average rate of change is a measure of the slope of the secant line in the closed interval [a,b]
average rate of change $=\frac{f\left(b\right)-f\left(a\right)}{b-a}$
here [a,b]=[5,6]
f(b)=f(6)=36+18-7=47
f(a)=f(5)=25+15-7=33
$⇒\frac{47-33}{6-5}=14$

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