HW 2.14 Mixed Derivatives

Front

What is the derivative of y = 11^x²?

Back

y' = 11^x² (2x)(ln 11)

Front

What is the value of the derivative of a constant function?

Back

0

Front

What is the formula for acceleration in terms of position?

Back

a = d²y/dx²

Front

If f'(x) > 0 and f''(x) < 0, what can be said about the function's behavior?

Back

The function is increasing but concave down.

Front

What is the relationship between a function and its inverse regarding derivatives?

Back

If g(x) = f⁻¹(x), then g'(x) = 1/f'(g(x)).

Front

How do you find the critical points of a function?

Back

Set the first derivative f'(x) = 0 and solve for x.

Front

What does it mean if the second derivative is zero at a point?

Back

It may indicate a point of inflection.

Front

What is the product rule for derivatives?

Back

If u and v are functions, then (uv)' = u'v + uv'.

Front

What is the chain rule for derivatives?

Back

If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

What is the significance of a tangent line in calculus?

Back

It approximates the function at a given point.