find the average rate of change of the function on the interval specified for real number c in simplest…

find the average rate of change of the function on the interval specified for real number c in simplest form. enter the missing part of the answer.\n\n$f(x)=2x^{2}-15$ on $-4,c$\n\n$\\frac{\\delta y}{\\delta x}=2c-$ _\n\nanswer

find the average rate of change of the function on the interval specified for real number c in simplest form. enter the missing part of the answer.\n\n$f(x)=2x^{2}-15$ on $-4,c$\n\n$\\frac{\\delta y}{\\delta x}=2c-$ _\n\nanswer

Answer

Explanation:

Step1: Find ( f(-4) ) and ( f(c) )

For ( f(x)=2x^{2}-15 ), when ( x = - 4 ), ( f(-4)=2\times(-4)^{2}-15=2\times16 - 15=32 - 15 = 17 ). When ( x = c ), ( f(c)=2c^{2}-15 ).

Step2: Use the average - rate - of - change formula

The average rate of change formula is (\frac{\Delta y}{\Delta x}=\frac{f(c)-f(-4)}{c - (-4)}=\frac{(2c^{2}-15)-17}{c + 4}). Simplify the numerator: ((2c^{2}-15)-17=2c^{2}-32). So (\frac{\Delta y}{\Delta x}=\frac{2c^{2}-32}{c + 4}). Factor the numerator: (2c^{2}-32 = 2(c^{2}-16)=2(c + 4)(c - 4)). Then (\frac{\Delta y}{\Delta x}=\frac{2(c + 4)(c - 4)}{c + 4}). Cancel out the common factor (c + 4) (assuming (c\neq - 4)), we get (\frac{\Delta y}{\Delta x}=2(c - 4)=2c-8).

Answer:

(8)