math grade 11
posted by priya .
A quadratic function is defined by
f(x)= 3x^2+4x2. A linear function is defined by g(x)= mx5. what values(s) of the slope of the line would make it a tangent to the parabola.

Slope of any function is first derivate of that function.
Quadratic function in your case have first dervate:
3*2*x+4=6*x+4
Linear function in your case have first dervate:
m
Line will be tangent of quadratic parabola when first derivates is egual.
m=6*x+4
m*x5=(6*x+4)*x5=6*x^2+4*x5
3*x^2+4*x2=6*x^2+4*x5
3*x^2+4*x6*x^24*x=5+2
3*x^2=3 Multiply with (1)
3*x^2=3 Divided with 3
x^2=1
x=+OR(1)
x1=1 , x2=1
Slope for x1=6*x1+4=6*(1)+4=6+4=2
Slope for x2=6*1+4=6+4=10
S1=2 S2=10