Let f(x)=(x+a)^n where a is a real number and n is a positive whole number, and n \geq2. If y=f(x) and y=f^{'}(x) are plotted on the same axes, the number of intersections between f(x) and f^{'}(x) will

Correct Answer is : always be even,

Oxford University MAT 2015 Solved Papers

Question : 2 of 10

Marks: +1, -0

Let

f(x)=(x+a)^n

where

a

is a real number and

n

is a positive whole number, and

n ≥2

. If

y=f(x)

and

y=f^{'}(x)

are plotted on the same axes, the number of intersections between

f(x)

and

f^{'}(x)

will

Solution:

f(x)

is an even function then

f^{'}(x)

will be an odd function, and vice versa.

f(x)

and

f^{'}(x)

will cross the

x

-axis at

(-a, 0)

and will have one further intersection when

y

and

x

are greater than 0 . The answer is (b).

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