Question

For the function

f(x) = sin x + sin² x

a). Write the equation for the first derivative, f'(x)

b). Write the equation for the tangent line to the curve at x=0

Answer 1

f(x) = sinnt sinn → f'on) = d (Sinnt asiman) du - Cosnt zodinncosn = Coont Sinan f'(o)= Cosot sino =1 Now aslope of tangent at n=0 is I { flo) = sino + sino = 0 tangent pass through 10,0) - Eqn of tangent line is yan

Answer 2

SOLUTION :

a.

f(x) = sin x + sin^2 x 

=> f’ (x) = cos x + 2 sin x cos x 

=> f’ (x) = cos x + sin 2x  (ANSWER).

b.

Slope of tangent at x = f ‘ (x) = cos x + sin 2x 

=> slope of tangent at x = 0, is = f’ (0) = cos 0 + sin 0 = 1 

Equation of tangent is :

y = x + c 

Since, point (0, 0) is on the curve,

=> 0 = 0 + c 

=> c = 0

Hence, equation of tangent at x = 0, is :

y = x  (ANSWER).