Question

7. What is the value of c which lies in [1, 2] for the function fx)=4x and g(x)=3x²​

Answer 1

Answer:

For f(x) the value of c is 4, and for g(x) the value of c is 3. i.e, value of x = 1, and y =2 at c.

Answer 2

Answer:

c=1.5

Step-by-step explanation:

We use Cauchy's Mean Value Theorm,

we have, $\frac{f(b) -f(a) }{g(b) -g(a)} =\frac{f'(c)}{g'(c)}$

Putting the values,

$\frac{4(2) -4(1) }{3(2)^{2} -3(1)^{2} } =\frac{4}{6c }$

$\frac{4 }{9} =\frac{4}{6c }$

$6c=9$

$c=\frac{3}{2}$

$c=1.5$