Between 1 and 2 , how many local maxima the function f (x) = 6x5 - 7x4 + 3x3 + 2x2 + 11 x - 17 has ?

Question

Between 1 and 2 , how many local maxima the function f (x) = 6x5 - 7x4 + 3x3 + 2x2 + 11 x - 17 has ? (A)  0  (B)  1  (C)  2  (D)  3

Tardigrade Admin · Accepted Answer

We have, f (x) =6x5-7x4+3x3+2x2+11x-17 f'(x) =30x4-28x3+9x2+4x+11 Here, f' (x) > 0 ∀ x ∈(1,2) ∴ f (x) is an increasing function for x ∈(1,2) Thus, f (x) has no local maxima ∀ x ∈ (1, 2)

Q. Between $1$ and $2$ , how many local maxima the function $f (x) = 6 x^{5} - 7 x^{4} + 3 x^{3} + 2 x^{2} + 11 x - 17$ has ?

$0$

$1$

$2$

$3$

We have, $f (x) = 6 x^{5} - 7 x^{4} + 3 x^{3} + 2 x^{2} + 11 x - 17$
$f^{'} (x) = 30 x^{4} - 28 x^{3} + 9 x^{2} + 4 x + 11$
Here, $f^{'} (x) > 0 \forall x \in (1, 2)$
$∴ f (x)$ is an increasing function for $x \in (1, 2)$
Thus, $f (x)$ has no local maxima $\forall x \in (1, 2)$

Q. Between 1 and 2 , how many local maxima the function f(x)=6x5−7x4+3x3+2x2+11x−17 has ?

0

1

2

3

We have, f(x)=6x5−7x4+3x3+2x2+11x−17 f′(x)=30x4−28x3+9x2+4x+11 Here, f′(x)>0∀x∈(1,2) ∴f(x) is an increasing function for x∈(1,2) Thus, f(x) has no local maxima ∀x∈(1,2)

Q. Between $1$ and $2$ , how many local maxima the function $f (x) = 6 x^{5} - 7 x^{4} + 3 x^{3} + 2 x^{2} + 11 x - 17$ has ?

$0$

$1$

$2$

$3$

We have, $f (x) = 6 x^{5} - 7 x^{4} + 3 x^{3} + 2 x^{2} + 11 x - 17$
$f^{'} (x) = 30 x^{4} - 28 x^{3} + 9 x^{2} + 4 x + 11$
Here, $f^{'} (x) > 0 \forall x \in (1, 2)$
$∴ f (x)$ is an increasing function for $x \in (1, 2)$
Thus, $f (x)$ has no local maxima $\forall x \in (1, 2)$