Question

differentiation question : show that the least value of x^2 + 2x(sinb) + 1 is cos^2b, where b is a constant.

Answer 1

f'(x) = 2x + 2sin(b) = 0 for critical values
x = -sinb
plug this into f(x)

= sin^2b -2sin^b + 1
= cos^2b

Answer 2

simplify the eqn as

(x+sinb)^2 + 1 - sinb^2

it will attain minimum value whwn the tyhing in the square is zero

hence the minimum value is 1-sinb^b or cosb^2

Answer 3

@jimmyrep my solution is better LOL

Answer 4

yup - good solution