### Home > CALC > Chapter 7 > Lesson 7.4.1 > Problem7-177

7-177.

Given: $f(x) = 5x^4 − 3x^2$

1. Write the equation of the tangent line to $f(x)$ at $x = 1$.

Use point-slope form of a line. $f(1)$ will give you the point, and $f^\prime(1)$ will give you the slope.

2. Use your tangent line to approximate $f(1.1)$.

Since a linear equation is easier to evaluate than a 4th-degree polynomial, use the tangent line to approximate $f(1.1)$.

3. Is the approximation an over or under estimate of the actual value?

Is the graph of $y = f(x)$ concave up or down $x = 1$?