Question

. Let f (x) be a function defined as follows:
f(x) = sin(x2 – 3x), x = 0; and 6x + 5x”, x > 0
Then at x = 0, f (x)
(a) has a local maximum (b) has a local minin
(c) is discontinuous
(d) none of these​

Answer 1

Answer:

Product 10 - 15 — -3/x2. 13. - 2/(2x - W 14. - 3/(3x + 1)2 15. -1/(x + 5)2 16. -I/(x _ 2)2 ... If 0 = 1t/6 then tan(1t/6) = 1/,}i Substituting yields: ... f(O) = 0 it follows that f(x) > 0 for all x with 0 < x < n/2.

Answer 2

f'(x)=2cos(x^2-3x)(2x-3)

f''(x)=2cos(x^2-3x)-(2x-3)^2(sin(x^2-3x)

Now f(x) has a critical point at x=0

so f'(x) =0 (exist)

=> when x=0

f"(0)= 2cos(0^2-3(0)) - (2(0)-3)^2 × (sin(0^2-3(0))

=2cos(0)-9sin(0)

=2(1)

=2>0

f has local minimum and point of minima at x=0

ANSWERE OPTION B