### Home > CALC3RD > Chapter Ch5 > Lesson 5.5.1 > Problem5-155

5-155.

Let $f(x) = 5x^4 - 3x^2$.

1. ​Write the equation of the line tangent to $y = f(x) \operatorname{at} x = 1$.

Use the slope, which is $f′(1)$, and the point $(1, f(1))$ to write the equation.

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

$≈ 3.4$

3. Is the approximation an overestimate or an underestimate of the actual value?

If $y = f(x)$ is concave up at $x = 1$, then the approximation is an underestimate.