First slide

Maxima and minima

Question

The point of inflection of $y = x^{3} - 5 x^{2} +$ $3 x - 5$ is

Moderate

A

$\frac{1}{2}$
B

$\frac{3}{4}$
C

$\frac{7}{4}$
D

$\frac{5}{4}$

Solution

Since $y$ is twice differentiable function so for inflection points $y^{''} (x) = 0, y^{'''} (x) \neq 0$
$y^{'} (x) = 3 x^{2} - 10 x + 3$
$y^{''} = 6 x - 10 . So, y^{''} (x) = 0 if x = \frac{5}{4}$
$y^{'''} (x) = 6 \neq 0 . So, x = \frac{5}{4}$ is a point of inflection.

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