Question

-what is the critical value of:
$x {}^{2} + 4x - 2 \geqslant 0$
​

Answer 1

Answer:

To determine the critical point, first find the derivative of the given function f(x),

f

′

(x)=

dx

d

x

3/5

(4−x)=

5x

2/5

4×3

−

5

8

x

3/5

=

5x

2/5

12−8x

Now, put f

′

(x)=0⇒x=

2

3

∴ Critical number for x is 3.

(2) A function f(x) is convex, if f

′′

(x)>0

⇒y=e

x

⇒y

′′

=e

x

, which is always greater than zero

∴ domain of convexity ∈R