Question

Find the average rate of change for the function over the given interval
y=4x^2 between x=0 and x=7/4

please explain steps

Answer 1

your job is to compute
\[\frac{f(\frac{7}{4})-f(0)}{\frac{7}{4}-0}\]

Answer 2

not hard in this example because\(f(0)=0\) giving
\[\frac{f(\frac{7}{4})}{\frac{7}{4}}\]

Answer 3

@satellite73 , it says "rate" so dont we have to find it's derivative?

Answer 4

\[f(\frac{7}{4})\times \frac{7}{7}=4(\frac{7}{4})^2\times \frac{4}{7}\]

Answer 5

"average rate"

Answer 6

so lost

Answer 7

so rate = derivative? slope?
idk..

Answer 8

\[4\times \frac{7}{4}\times \frac{7}{4}\times \frac{4}{7}=4\times \frac{7}{4}=7\]

Answer 9

@yomamabf
average rate is like the slope of a line

Answer 10

\[m=\frac{y_2-y_1}{x_2-x_1}\]

Answer 11

your function is not a line, but you have two points on the curve, namely \((0, f(0))\) and \((\frac{7}{4},f(\frac{7}{4}))\)

Answer 12

so the answer is 1/3

Answer 13

since \(f(0)=0\) your two points are \((0,0)\) and \((\frac{7}{4},\frac{49}{4})\)

Answer 14

no not 1/3, rather
\[\frac{\frac{49}{4}}{\frac{7}{4}}=\frac{49}{4}\times \frac{4}{7}=7\]

Answer 15

thanku