Math · Calculus · Worked example

Derive the slope of x² at 2

Find the tangent slope for f(x)=x² at x=2.

Form the quotient

Use the output change between 2 and 2+h.

\frac{{(2 + h)}^{2} - 4}{h}

For h≠0, factor h out of the numerator before cancelling.

\frac{4 h + h^{2}}{h} = 4 + h

The simplified expression tends to 4 from either side.

f^{'} (2) = 4

The point is (2,4); use point-slope form.

y - 4 = 4 (x - 2)

The slope is 4 and the tangent is y=4x−4.

Find the tangent to x² at x=−1.

Show the answer and explanation

The derivative is 2x, giving slope −2 at the point (−1,1).

Change an input and predict the result before checking it.

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