Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
Equation of normal drawn to the graph of the function defined as =\frac{\sin x^{
Equation of normal drawn to the graph of the function defined as \( f(x)=\frac{\sin x^{2}}{x} \) \( \boldsymbol{x} \neq \mathbf{0} \) and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \) at the origin is?
- A. \( x+y=0 \)
- B. \( x-y=0 \)
- C. \( y=0 \)
- D. \( x=0 \)
Step-by-step solution
At the origin, f(0)=0. The derivative f'(0) = lim_{h→0} sin(h^2)/h^2 = 1, so the slope of the tangent is 1. The slope of the normal is -1. The normal passes through (0,0), so its equation is y = -x, i.e., x+y=0.
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