Question

(1 point) Consider the function f(x)=2x3−6x2−48x+5 on the interval [−4,10]. Find the average or mean slope of the function on this interval.

Answer 1

Answer:

The mean slope on the interval is 68

Step-by-step explanation:

The formula to find the mean slope on an interval [a, b] is given by:

$\frac{f(b)-f(a)}{b-a}$

So now, we are going to find f(10) and f(-4) and will substitute these values in the formula.

$f(10)=2(10)^{3} -6(10)^{2} -48(10)+5\\f(10) =2(1000)-6(100)-480+5\\f(10)=2000-600-480+5\\f(10)=925\\\\f(-4)=2(-4)^{3} -6(-4)^{2} -48(-4)+5\\f(-4)=2(-64)-6(16)+192+5\\f(-4)=-128-96+192+5\\f(-4)=-27$

So the mean slope of the function on the interval [-4,10] is:

$\frac{f(10)-f(-4)}{10-(-4)} =\frac{925-(-27)}{14} =\frac{925+27}{14} =\frac{952}{14} =68$