differentiation question

[adam2016]

hey guys,

I'm in a pickle here,I have a maths exam tomorrow and just looking for help,but I am not breaking the rules as calculus or differentiation has it's uses in programming and computer science and the maths module is apart of my computer science degree

any way here is the question find the point on the curve y = 4x^2 + 2x + 7 where the tangent makes an angle of 45 degress with the positive x axis

I thought I would first differentiate and set it equal to zero but this way I am nit left with a quadratic so I can't solve it by finding factors,

any advice?

[lastchance]

I thought I would first differentiate and set it equal to zero

No, set the derivative equal to 1 (or, possibly, -1).
tan(45 deg) = 1
tan(-45 deg) = -1

This gives you x. (It's just a linear equation.) Then substitute in the curve equation for y.

[adam2016]

thanks lastchance much appreciated! :)

justa quick follow up how did you get 45 degrees = 1?

thanks

[adam2016]

also just did the equation is the answer x = 0.75 and y = 3.25?

also just wondering how did you know when to just differentiate and solve a linear equation? they word it in quite a tricky way in the exam

[lastchance]

adam2016 wrote:

justa quick follow up how did you get 45 degrees = 1?

I didn't. Read carefully.

The derivative gives you the SLOPE, or TANGENT of the angle.

tan(45 deg) = 1, NOT 45 deg = 1

also just wondering how did you know when to just differentiate and solve a linear equation?

If you differentiate 4x² + 2x + 7 you will get 8x+2
If you set that equal to 1 then 8x+2=1 (a linear equation, with solution x=-1/8 = -0.125) ... assuming you want positive slope. There is a negative-slope solution, too (your question is extremely badly phrased), from 8x+2=-1 (with solution x=-3/8=-0.375).

[adam2016]

thanks last chance

and agreed for me anyway they can be quite tricky to decipher,would make life easier if they were just differentiate the following etc

[Ganado]

Just practice it a few times with different numbers/angles (that you can do self-checks against), and you'll become comfortable with it.

For example, are you comfortable with the following:
Find the equation of the line that is tangential to the curve y = x^3 + 2 x^2 + 1 @ x = -1.

Also, not sure if this is part of your curriculum, but you also might want to find the line normal (perpendicular) to the same line & point. In 2d, the perpendicular line of y = mx + b has a slope (-1/m).