PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
Share

Books Shortlist

# Solution for Prove that the Function F(X) = X3 − 6x2 + 12x − 18 is Increasing on R ? - PUC Karnataka Science Class 12 - Mathematics

#### Question

Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?

#### Solution

$f\left( x \right) = x^3 - 6 x^2 + 12x - 18$

$f'\left( x \right) = 3 x^2 - 12x + 12$

$= 3\left( x^2 - 4x + 4 \right)$

$= 3 \left( x - 2 \right)^2 \geq 0, \forall x \text { in R } \left[ \because 3 > 0 \text { &} \left( x - 2 \right)^2 \geq 0 \right]$

$\text { So,f(x)is increasing on R } .$

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [3]

Solution Prove that the Function F(X) = X3 − 6x2 + 12x − 18 is Increasing on R ? Concept: Increasing and Decreasing Functions.
S