(1 point) Consider the function f(x)=2x3−9x2−60x+1 on the interval [−4,9]. Find the average or mean slope of the function on this interval. Average slope: By the Mean Value Theorem, we know there exists at least one value c in the open interval (−4,9) such that f′(c) is equal to this mean slope. List all values c that work. If there are none, enter none . Values of c:

c = 4.97 and c = -1.97

Step-by-step explanation: Mean Value Theorem states if a function f(x) is continuous on interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:

So, for the function f(x) = on interval [-4,9]

f(-4) =

f(-4) = 113

f(9) =

f(9) = 100

Calculating average:

Resolving through Bhaskara:

c =

c = = 4.97

c = = -1.97

Both values of c exist inside the interval [-4,9], so both values are mean slope: c = 4.97 and c = -1.97

77

step-by-step explanation:

a is the correct