Let m denote the slope of the tangent to the curve y=X^3 - 4x^2 +x +4 at the point (-1 , -2) . If the slope of the tangent to the curve y=3x^2 + ax + b at (2 , 0) on the curve is m , dertermine the values of a and b.

Question

Let m denote the slope of the tangent to the curve y=X^3 - 4x^2 +x +4 at the point (-1 , -2) . If the slope of  the tangent to the curve y=3x^2 + ax + b at (2 , 0) on the curve is m , dertermine the values of a and b.

anonymous · Answer

@Arnab09 @FoolForMath @experimentX @eliassaab @yash2651995

lgbasallote · Answer

are you allowed to use derivatives?

anonymous · Answer

yes

yash2651995 · Answer

m=12?
a=0? 
b=any value?

yash2651995 · Answer

b will have a fixed value.. (2,0) should satisfy that equation

yash2651995 · Answer

b=-12?

anonymous · Answer

@yash2651995  u r correct a=0  b=-12   how?????

anonymous · Answer

@yash2651995  can u show me wat u have done...

yash2651995 · Answer

first equation.. f(x)=y=X^3 - 4x^2 +x +4
f'(x)=3x^2-8x+1
at (-1,-2) x=-1 so put its value here^
f'(x)=m i.e. instantaneous slope at that point
that gives m=12
now differentiate second eq g(x)=y=3x^2 + ax + b 
g'(x)=6x+a   =m at (x,y)= (2,0) (,given)
12+a=m=12 
ie a=0
now g(x) has to satisfy (2,0) as the point will be on it as we are asked about slope on it.. 
now, y=3x^2 + ax + b 
a=0
x=2 
y=0
means b=-12

anonymous · Answer

May i have help