Pls help ASAP in all 18.19.The curve y = x³ — 3x² + 2 has an inflection point at the point:a) P(1, 0)b) P(-1, -2)c) P(1,4)The interval where the curve y =a) x < 1b) neverex + 1ex-1d) none of theseis decreasing is:c) (-∞0,00)d) none of these

18) Given that : We have to find the point of inflection of the given…

Answered: 18. 19. The curve y = x³ – 3x² + 2 has…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Pls help ASAP in all

18.
19.
The curve y = x³ — 3x² + 2 has an inflection point at the point:
a) P(1, 0)
b) P(-1, -2)
c) P(1,4)
The interval where the curve y =
a) x < 1
b) never
ex + 1
ex-1
d) none of these
is decreasing is:
c) (-∞0,00)
d) none of these

Expert Solution

Step 1: ''Introduction to the solution''

18) Given that : $y equals left parenthesis x cubed minus 3 x squared plus 2 right parenthesis............ left parenthesis 1 right parenthesis$

We have to find the point of inflection of the given function.

Differentiating (1) with respect to 'x' we get, $fraction numerator d y over denominator d x end fraction equals 3 x squared minus 6 x$

Again, differentiating with respect to 'x' to obtain, $fraction numerator d squared y over denominator d x squared end fraction equals left parenthesis 6 x minus 6 right parenthesis$

For point of inflection, $fraction numerator d squared y over denominator d x squared end fraction equals left parenthesis 6 x minus 6 right parenthesis equals 0 rightwards double arrow x equals 1$

Putting $x equals 1$ in $left parenthesis 1 right parenthesis space$ to obtain the point of inflection of $f$ is $P left parenthesis 1 comma 0 right parenthesis$ . So,. option(a) is Correct.