How do you solve a difference quotient example?

Examples Using Difference Quotient Formula Example 2 : Find the derivative of f(x) = 2×2 – 3 by applying the limit as h → 0 to the difference quotient formula. By applying the limit as h → 0, we get the derivative f ‘ (x). f ‘(x) = 4x + 2(0) = 4x. Answer: f ‘ (x) = 4x.

How do you simplify fractions?

You can simplify a fraction if the numerator (top number) and denominator (bottom number) can both be divided by the same number. Six twelfths can be simplified to one half, or 1 over 2 because both numbers are divisible by 6. 6 goes into 6 once and 6 goes into 12 twice.

How to find and simplify difference quotient?

– Plug x + h into the function f and simplify to find f ( x + h ). – Now that you have f ( x + h ), find f ( x + h) – f ( x) by plugging in f ( x + h) and f – Plug your result from step 2 in for the numerator in the difference quotient and simplify.

How do you simplify a quotient?

– All exponents in the radicand must be less than the index. – Any exponents in the radicand can have no factors in common with the index. – No fractions appear under a radical. – No radicals appear in the denominator of a fraction.

How do I use the difference quotient?

We first calculate f (x+h). f (x+h) = 2 (x+h)^2+(x+h) – 2

We now substitute f (x+h) and f (x) in the difference quotient\\dfrac {f (x+h) – f (x)} {h} =\\dfrac { 2 (x+h)^2

We expand the expressions in the numerator and group like terms. =\\dfrac { 4 x h+2 h^2+h} {h} = 4 x+2 h+1

How to find difference quotient calculator?

Substitute f (x) with f (x+h).

Now subtract f (x) from f (x+h); f (x+h) – f (x)

Open the brackets and simplify this expression.

Divide this reduced expression by h. The value so obtained will be the difference quotient of the given function.