Exams › JEE Advanced › Maths
If (f'(x)\le 0) for all (x) in the interval ([0,b]), and (f(c)=0), then (f(x)) intersects the x-axis only once at (x=c). What is true about the root at (x=c)?
- f'(x) is non-positive
- f(c) equals zero
- x = c is a triple root
- The derivative at x = c is zero
Correct answer: f(c) equals zero
Solution
A point where the graph intersects the x-axis is a root, which means the function value there is zero. The statement already gives (f(c)=0), so the correct option is that (f(c)) equals zero.
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