   Chapter 2.3, Problem 101E

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# For what values of a and b is the line 2 x + y = b tangent to the parabola y = a x 2 when x = 2 ?

To determine

To find:

a and b such that the given line is a tangent to parabola at x =2

Explanation

Formula:

(a) Constant multiple rule: ddxkx=k.ddxx      where k is constant.

(b) Power rule:

ddxxn=nxn-1

Calculation:

Slope of line y=mx+c is m.

Therefore, slope of line y=b-2x is -2…….(1)

Tangents at x to the parabola y=ax2 has slope dydx.

Now dydx=ddxax2

By using constant multiple and power rule,

dydx=ddxax2=2ax

dydx=2ax…… (2) Thus slope of a tangent at a point x is 2ax

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