Question

Find the value of c such that the line y=3/2x+6 is tangent to the curve

Answer 1

Line y = 3/2 x + 6 has slope = 3/2 

Let f(x) = c√x 
Then f'(x) = c/(2√x) 

Now we need to find values of x and c so that 
slope of curve at x = slope of line 
f'(x) = 3/2 
c/(2√x) = 3/2 
c = 3√x 

Substituting this back into equation of curve, we get 
f(x) = c√x = (3√x)√x = 3x 

Now we find x where f(x) intersects line 3/2 x + 6 
3x = 3/2 x + 6 
6x = 3x + 12 
3x = 12 
x = 4 

c = 3√x = 3√4 = ±6 

When c = -6, f(x) = -6√x and f'(x) = -3/√x < 0. 
But slope of line = 3/2 > 0 

Therefore c = -6 is not valid 


ANSWER: c = 6 
i hope this will help you