Question

Slope of a normal at x = a on the graph of f(x) is -1/2. If the rate of rate of change of f(x) at the point a is $\alpha$ , find the value of $4{\alpha }^2.$

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Answer 1

We want to find the rate of change of f(x) at the point a. Rate of change of f(x) at a point is the instantaneous rate of change. We saw that instantaneous rate of change is given by the slope of the tangent. In question, we are given the slope of the normal. From this we can find the slope of the tangent or the rate of change.

If m is the slope of the normal, then slope of tangent is given by (-1/m).

= 2

We are asked to calculate $4{\alpha }^2$

= 4 $\times$ 4 = 16