The average rate of change of a function f(x)f from x=a to x=b is the slope of the line which passes through (a, f(a) and (b, f( consider the function f(x)=x^2+6 and find the following: (a) the average rate of change of f(x) from x=−1 to x=4. (b) the average rate of change of f(x) from x=a to x=b. (c) the average rate of change of f(x)f between the points (x, f(x)) and (x+h, f(x+ assume h> 0

a) 3

b) b + a

c) 2x + h

Step-by-step explanation:

Since, The average rate of change of a function f(x)f from x=a to x=b is the slope of the line which passes through (a,f(a) and (b,f(b)), we can write the formula for Average Rate of Change as:

Part a)

The average rate of change of f(x) from x = −1 to x = 4. Using these values in above formula, we get:

Thus, the average rate of change of f(x) from x = −1 to x = 4 is 3

Part b)

The average rate of change of f(x) from x=a to x=b. Using the values in the above formula, we get:

Thus, the average rate of change of f(x) from x = a to x = b is b + a

Part c)

The average rate of change of f(x) between the points (x,f(x)) and (x+h,f(x+h)). Using the values in above formula, we get:

Thus, The average rate of change of f(x) between the points (x,f(x)) and (x+h,f(x+h)) is 2x + h.

step-by-step explanation:

y=mx+b

step-by-step explanation:

m slope

b y-intercept