Let f(x) = 4x³ − 5x² + 7x − 2. Find f′(2). Give the answer as an integer.

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Slope of a cubic

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Let $f (x) = 4 x^{3} - 5 x^{2} + 7 x - 2$ . Find $f^{'} (2)$ . Give the answer as an integer.

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Hint

Differentiate each term separately, then substitute.

Solution

Differentiate term by term with the power rule: $f^{'} (x) = 12 x^{2} - 10 x + 7$ .
At $x = 2$ the terms are $12 \times 4 = 48$ , $10 \times 2 = 20$ and $7$ .
Hence $f^{'} (2) = 48 - 20 + 7 = 35$ .

Answer: $35$