Question Video: Finding and Evaluating the Rate of Change of Polynomials Mathematics • Higher Education

Find the rate of change of 𝑓(π‘₯) = π‘₯Β² βˆ’ 3π‘₯ + 2 at π‘₯ = 5.

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Video Transcript

Find the rate of change of 𝑓 of π‘₯ equals π‘₯ squared minus three π‘₯ plus two at π‘₯ equals five.

The rate of change can be calculated by differentiating to work out 𝑑𝑦 by 𝑑π‘₯ or 𝑓 dash π‘₯. In this example, 𝑓 of π‘₯ is equal to π‘₯ squared minus three π‘₯ plus two. Differentiating this gives us 𝑓 dash of π‘₯ is equal to two π‘₯ minus three as the differential of π‘₯ squared is two π‘₯, the differential of negative three π‘₯ is negative three, and the differential of two is zero.

We want to calculate the rate of change at π‘₯ equals five. Therefore, 𝑓 dash of five is equal to two multiplied by five minus three. Two multiplied by five is 10 minus three equals seven.

This means that the rate of change of 𝑓 of π‘₯ at π‘₯ equals five is equal to seven.

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