### Home > CALC > Chapter 6 > Lesson 6.3.1 > Problem 6-87

Consider the function

*f*(*x*) = −3^{x}^{ }. Homework Help ✎Find the equation of the tangent line to

*f*(*x*) = −3^{x}^{ }at*x*= 0.Approximate

*x*= 0.1 using part (a).Use

*f*″(*x*) to justify whether part (b) is an under or over approximation of the actual value.

Evaluate *f* '(0) to find the slope, and evaluate *f*(0) to find the *y*-intercept. Use the point-slope formula to create the equation of the tangent line.

Use the tangent line at *x* = 0 to evaluate *x* = 0.1. This will approximate *f*(0.1). Why approximate?

Since a tangent is a linear equation, it is easier to evaluate than *f*(x).

A concave up graph has tangent lines that are below the curve. Sketch it, you will see.

And a concave down graph has tangent lines that are above the curve.

Overestimate since *f* ''(0) = −(ln 3)^{2} · 3^{0} = −(ln 3)^{2} < 0