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.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°