If the tangent to the function y = f(x) at (3,4) makes an angle of (3 π /4) with the positive direction of x-axis in anticlockwise direction then f ' (3) is

Question

If the tangent to the function y = f(x) at (3,4) makes an angle of (3 π /4) with the positive direction of x-axis in anticlockwise direction then f ' (3) is (A) -1 (B) 1 (C) (1/√3) (D) √3

Tardigrade Admin · Accepted Answer

Given y = f ( x ) Differentiating w.r.t x, we get y'=f'(x) which is the slope of the tangent f'(3)= tan (3 π/4)=- tan (π/4)=-1 Hence, f'(3)=-1.

Q. If the tangent to the function $y = f (x)$ at $(3, 4)$ makes an angle of $\frac{3 π}{4}$ with the positive direction of x-axis in anticlockwise direction then $f^{'} (3)$ is

$- 1$

$1$

$\frac{1}{3}$

$3$

Given $y = f (x)$
Differentiating w.r.t $x$ ,
we get $y^{'} = f^{'} (x)$
which is the slope of the tangent
$f^{'} (3) = tan \frac{3 π}{4} = - tan \frac{π}{4} = - 1$
Hence, $f^{'} (3) = - 1$ .

Q. If the tangent to the function y=f(x) at (3,4) makes an angle of 43π​ with the positive direction of x-axis in anticlockwise direction then f′(3) is

−1

1

3​1​

3​

Given y=f(x) Differentiating w.r.t x, we get y′=f′(x) which is the slope of the tangent f′(3)=tan43π​=−tan4π​=−1 Hence, f′(3)=−1.

Q. If the tangent to the function $y = f (x)$ at $(3, 4)$ makes an angle of $\frac{3 π}{4}$ with the positive direction of x-axis in anticlockwise direction then $f^{'} (3)$ is

$- 1$

$1$

$\frac{1}{3}$

$3$

Given $y = f (x)$
Differentiating w.r.t $x$ ,
we get $y^{'} = f^{'} (x)$
which is the slope of the tangent
$f^{'} (3) = tan \frac{3 π}{4} = - tan \frac{π}{4} = - 1$
Hence, $f^{'} (3) = - 1$ .