Sign up to access problem solutions.

Already have an account? Log in here.

You don't need a calculator or computer to draw your graphs! Derivatives and other Calculus techniques give direct insights into the geometric behavior of curves.

How many real values of \(x\) satisfy the equation

\[\large {x}^{2}-{2}^{x}=0? \]

Sign up to access problem solutions.

Already have an account? Log in here.

\[6 \ln (x^2 + 1) - x = 0 \]

How many real solutions exist for the equation above?

Sign up to access problem solutions.

Already have an account? Log in here.

Sign up to access problem solutions.

Already have an account? Log in here.

Let \(f(x)=x^4-6x^2+5.\) If \(P(x_0,y_0)\) is a point such that \(y_0>f(x_0)\) and there are exactly **two distinct tangents** drawn to the curve \(y=f(x),\) what is the maximum value of \(y_0?\)

Try : Part-2

Sign up to access problem solutions.

Already have an account? Log in here.

The function \(f(x)= x^{3}-11x^{2} +19x+13\) has zeros \(a_{1},a_{2},a_{3}.\) Then what is the value of \([ a_{1} ]+[ a_{2} ]+[ a_{3} ]?\)

**Note:** \([m]\) Represents the greatest integer less than or equal to \(m.\)

Sign up to access problem solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...