A maths - Differentiation

bonkysleuth SG

1 Show that the function f(x) = x^3 - 3x^2 + 9x -5 is increasing with x for all real values of x.

My answer is

As f'(x) = 3((x-1)^2 +2) >/= 0, f(x) is increasing with x for all real values of x. Do check my answer because I seem to obtain a different answer from the TYS and I still think mine if correct. (I double-checked numerous times)

2 Find the gradient of the tangent to the curve y =x cos x at the point where x = 0.5, giving your answer to 2 decimal places

In degree mode, I got 1.00, but in radian answer is 0.64. I remember having heard my teacher said there are some topics/questions that you HAVE to use radian mode no matter what. Are questions like the above supposed to be done in radian mode? (the answer is TYS is the one in rad)

Thanks

TenSaru SG

1) I think the expression is correct but it is strictly >0.

2) Use radian mode whenever you differentiate a trigo function.

OHSheet SG

Q1.

f(x) = x^3 - 3x^2 + 9x -5

therefore, f'(x) = 3x^2 -6x +9

for all real numbers, for x>0, f'(x) is >0 therefore, the function f(x) is increasing for all values of x>0..

u can also use graphmatica to check this, to show that the curve is increasing for all x>0.

Q2.

y=xcosx

therefore,

y' =x(-sinx) + cosx(1)

y' = cosx - xsinx

at x=0.5...

subt and solve for the value

Its usually obvious. for an angle less than 6.28 (2pi), you can suspect that it requires you to express it in rad. Just base it on instincts. thats how i do it. Besides, if the range of the graph is provided, then it also serves as a guide..

eg... the question should go.....

solve for grad tangent for y= xcosx at the point x=0.5 in the range of eg.. o<x<2pi.

Besides, just think... with the horz axis in degree, 0.5 is ridiculously small to be considered, therefore, you can outrule deg mode.

Garrick_3658 SG

Correct.

With practice, you will be able to differentiate between the use of radian and degree, the most obvious being they didn't put x=0.5 DEGREES, but just 0.5 alone. True, they didn't state 0.5 rad either, but usually most degree questions will require the DEGREE symbol to be stated.