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

Find the rate of change of π(π₯) = π₯Β² β 3π₯ + 2 at π₯ = 5.

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### Video Transcript

Find the rate of change of π 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 ππ¦ by ππ₯ or π dash π₯. In this example, π of π₯ is equal to π₯ squared minus three π₯ plus two. Differentiating this gives us π 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, π 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 π of π₯ at π₯ equals five is equal to seven.