CMI Data Science 2025 | Part A | Question: 12

Question

Let $f(x)=\sqrt{x}$. We draw a tangent to the curve $y=f(x)$ at the point on the curve whose $x$ coordinate is equal to $4$. Where does this tangent intersect the $X$-axis?

• A. $x=4$
• B. $x=-2$
• C. $x=-4$
• D. $x=2$

Answer 1

We know, 
y = m.x + c..{Line passing through the point (x,y), having the c as its y intercept)
So, d(y)/dx = m...!{Where m is the slope of the Tangent Line..!

So, 1/(2).root(x) = m 
So, for x=4...
m = 1/4...!!

So, now, 
(y - y0) = m.(x- x0)
(2 - 0) = 1/4.(4 - x0)
So, 8 = 4 - x0
So, x0 = -4..!!