Home › JEE Main › mathematics › Application of Derivatives › The slope of the normal to the curve $y = f(x)$ …
The slope of the normal to the curve $y = f(x)$ at $x = a$ is:
A$f(a)$
B$\dfrac{1}{f(a)}$
C$f'(a)$
D$-\dfrac{1}{f'(a)}$
Answer & Solution
Correct answer: D. $-\dfrac{1}{f'(a)}$
The normal is perpendicular to the tangent, so its slope is −1/f'(a).
Related questions
Elasticity of demand is given byProfit is maximised whereMarginal revenue (MR) for a price-taking firm (perfect competition) equalsMarginal cost (MC) isTwo numbers have a sum of $24$. Their product is largest when the numbers areFor $f(x)=3x^4-8x^3+12x^2-48x+25$ on $[0,3]$, the critical point inside the interval isA cylindrical tank of radius $10$ m is filled with wheat at $314$ m$^3$/h. The depth of thThe maximum value of $[x(x-1)+1]^{1/3}$ for $0\le x\le 1$ is