Tuesday

July 29, 2014

July 29, 2014

Posted by **Amponsah** on Monday, April 9, 2012 at 4:35am.

i) the values of a and b

ii) the equation of the curve

- calculus -
**Reiny**, Monday, April 9, 2012 at 9:50amsince dy/dx = ax^2 + b

the equation must have been

y = (1/3)a x^3 + bx + c

at (1,-11) ---> -11 = (1/3) a + b + c

or

a + 3b + 3c = -33 (#1)

at (2, -16) ---> -16 = (8/3)a + 2b + c

or

8a + 6b + 3c = -48 (#2)

#2 - #1 :

7a + 3b = -15 (#3)

We also know that at (2,-16), the slope is zero

ax^2 + b = 0

4a + b = 0

b = -4a

sub into #3

7a - 12a = -15

-5a=-15**a=3**

then b= -12

and in #1

3 -36+ 3c = -33

3c = 0

c = 0

function is y = (1/3)(3)x^3 - 12x

y = x^3 - 12x

**Related Questions**

calculus - Suppose y is defined implicitly as a function of x by x^2+Axy^2+By^3=...

Math - How can I determine a value of gradient from a graph if the line is ...

Maths: Intergration - The curve with equation y = ax^2 + bx + c passes through ...

Maths - a curve ahs parametric equations x=t^2 and y= 1-1/2t for t>0. i)find ...

calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...

Calculus - Damon - Find the line which passes through the point (0, 1/4) and is ...

Calculus Help Please!!! Check - A curve passes through the point (0, 2) and has...

12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...

calculus - the tangent line to the curve y=x^2 at the point (a,a^2) passes ...

calc - The slope of the tangent to the curve y=f(x) is given by (1/9)(x^2)(y^2...